Computer Science
Scientific paper
Jul 2003
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003nonli..16.1449m&link_type=abstract
Nonlinearity, Volume 16, Issue 4, pp. 1449-1471 (2003).
Computer Science
3
Scientific paper
Bifurcation from spherical symmetry occurs transcritically when the degree l of the spherical harmonics is even. In this case the leading-order bifurcation equations are completely determined by the symmetry. Several new results are presented concerning the existence or non-existence of solutions with dihedral symmetry in two-dimensional subspaces. For large l, there is an alternating arrangement of existence and non-existence of such solutions. Although all bifurcating branches of stationary solutions are unstable, a preferred solution is identified using a variational criterion; this solution also has only one positive eigenvalue. It is shown that the axisymmetric state is never the preferred solution according to this criterion. Results on the existence and stability of solution branches are given for even values of l up to l = 18, including all solutions in subspaces of dimension three or lower. For l = 6, 10 and 12, the preferred solution has icosahedral symmetry.
No associations
LandOfFree
Transcritical bifurcation with <B>O</B>(3) symmetry does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Transcritical bifurcation with <B>O</B>(3) symmetry, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Transcritical bifurcation with <B>O</B>(3) symmetry will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-1884920